I'm not saying 10-15% isn't a big deal. The meters need to be fixed, but 10-15% isn't 600%.
If lighting is not the main driver of your energy usage, then there is no way replacing your light bulbs with LEDs is going to increase the metered energy usage. Even if the LEDs are causing your meter to over-report, which would likely only happen under ideal conditions that are not your case, the energy saved by switching away from incandescents would more than make up for it and you'd still wind up with a lowered bill. Given that lighting isn't the main component of your energy usage, it's unlikely you'd have this issue at all.
I pulled that 10-15% figure out of nowhere, but it's an educated guess for the kind of effect you might see under ideal conditions for an actual household that might actually exist. You'd still have to use identical LED bulbs behind dimmers set to the same dim setting and have that be a significant portion of your energy consumption to get a significant effect with the flawed meters. It's difficult to say exactly what the effect with mixed loads will be, but the tests in the article have all the hallmarks of a pathological scenario, and my opinion it's all going to be mostly a wash for the majority of people.
On the other hand, it's worth noting that typical AC dimmers, in general, tend to be terrible from an electrical engineering standpoint. Meter shenanigans aside (though for the same reasons), they also cause tons of RF interference and have other issues, and often significantly shorten the lifespan of whatever bulbs you connect them to. You're beter off with DC/PWM dimming (e.g. lights with built in brightness control, not standalone AC dimmers) or smart bulbs.